A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2 M as shown in the figure. The block and the man are resting on a rough wedge of mass M as shown in the figure. The whole system is resting on a smooth horizontal surface. The man pulls the rope. Pulley is massless and frictionless. What is the displacement(in m ) of the wedge when the block meets the pulley ? (Man does not leave his position during the pull) (on the block 2 M.)

Question

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2 M as shown in the figure. The block and the man are resting on a rough wedge of mass M as shown in the figure. The whole system is resting on a smooth horizontal surface. The man pulls the rope. Pulley is massless and frictionless. What is the displacement(in m ) of the wedge when the block meets the pulley ? (Man does not leave his position during the pull) (on the block 2 M.) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c053e07873d6e6567ac76d178b89a40a-.png" /> Δ x cm =0 ⇒ M (2- x )=3 M ( x ) 4 x =2 ⇒ x =(1/2) m

Δxcm​=0 ⇒M(2−x)=3M(x)4x=2 ⇒x=21​m

$Δ x_{c m} = 0$
$\Rightarrow M (2 - x) = 3 M (x) 4 x = 2$
$\Rightarrow x = \frac{1}{2} m$